This might be an issue with your permalinks. Can you set it to Postname under Settings > Permalinks and see if you get the same thing? If so, can you share temp admin access to your site so we can check? You can post the details here using the private reply option below.
Problem solved. OMG.
My server hosting provider had the wpsite permissions wrong.
I am posting this so that you will know, and that anyone looking will know as well.
The tipoff was that ANY publish of anything at all caused the problem.
It was not Beaver Builder at all.